Research Fellows Directory
Professor Gui-Qiang Chen
University of Oxford
Partial Differential Equations (PDEs) are key equations for anyone wanting to use maths to solve real life problems. This is because they describe change, and change of course happens all around us all of the time. Mathematical descriptions of physical systems are typically phrased in terms of rates of change, or derivatives. A PDE is an equation involving the derivatives of a function, and solving it amounts to finding the function itself. What is exciting about PDEs is their universal applicability and their flexibility in allowing us to try to model and understand changes in different systems. Two of the prototypes are the fundamental systems of fluid dynamics: the Euler equations and the Navier-Stokes equations, respectively. Their mathematical treatment presents severe difficulties, since their solutions may develop singularities such as shock waves and other discontinuities. Our recent research efforts have continued to be in such an area toward mathematical research on nonlinear PDEs and related applications, along with the analysis and development of efficient nonlinear methods. Given the richness and range of applications of nonlinear PDEs, this research project will have a broad impact by investigating important nonlinear PDEs and related applications and by developing methodology and a set of nonlinear techniques for their further study. Furthermore, the project will
(i) yield new deeper understanding of the mathematics of gases, fluids, and geometry, which is critical for aerodynamics, industrial gas processing, computer sciences, medical imaging, protein folding/unfolding, and environmental science;
(ii) open up new research opportunities for outstanding problems in this direction;
(iii) provide advanced training for graduate students and postdocs and enhance collaborations with junior researchers including members from underrepresented group; and
(iv) disseminate results via the websites, workshops, advanced courses, lectures, and publications.